Thermodynamics: common doubts, answered
The questions students ask most often about Thermodynamics, each with a short answer. For the full chapter, read the Thermodynamics notes.
Heat as energy: what thermodynamics studies
Read this section in the notes →How is thermodynamics different from kinetic theory?
Thermodynamics describes a system through large-scale quantities such as pressure, volume, temperature and internal energy, without referring to molecules at all. Kinetic theory explains those same quantities from the motion of molecules. Thermodynamics is therefore a macroscopic description, and its laws hold whatever the system is made of.
Thermal equilibrium and the zeroth law
Read this section in the notes →What does the zeroth law of thermodynamics say?
It says that if two systems are each in thermal equilibrium with a third, they are in thermal equilibrium with each other. This is what makes temperature a meaningful quantity: two bodies are in equilibrium exactly when they have the same temperature. It also justifies using a thermometer, which acts as the third system.
Internal energy, heat and work
Read this section in the notes →Why is it wrong to say a hot body contains a lot of heat?
Because heat is energy in transit, not something a body holds. A body contains internal energy; heat is the energy that flows into or out of it because of a temperature difference. Once the transfer stops, it no longer makes sense to call any part of that energy heat. The same applies to work.
Is internal energy a state variable while heat and work are not?
Yes. Internal energy depends only on the present state of the system, so its change between two states is the same along any path. Heat and work depend on the path taken: two different processes between the same states can involve different amounts of each, even though ΔU is the same.
Does the kinetic energy of a moving gas container count as internal energy?
No. Internal energy is measured in the frame where the system's centre of mass is at rest. It includes the random motion of molecules and their mutual potential energy, but not the motion of the system as a whole. A gas cylinder on a moving train has the same internal energy as one standing still at the same temperature.
First law of thermodynamics
Read this section in the notes →What is the sign convention in the first law of thermodynamics?
In ΔQ = ΔU + ΔW, ΔQ is positive when heat is supplied to the system, and ΔW is positive when the system does work on its surroundings, as in expansion. Work done on the system, as in compression, is negative. Some books use the opposite sign for work, so always check which convention a formula assumes.
Does supplying heat always raise the internal energy?
No. By the first law, ΔU = ΔQ − ΔW, so if the system does as much work as the heat it receives, its internal energy stays the same. That is what happens when an ideal gas expands isothermally. Internal energy rises only when the heat supplied exceeds the work done by the system.
Specific heat capacity
Read this section in the notes →Why is C_p greater than C_v for a gas?
At constant volume all the heat supplied goes into raising the internal energy. At constant pressure the gas also expands and does work on its surroundings, so extra heat is needed for the same temperature rise. For an ideal gas the difference per mole is C_p − C_v = R.
State variables and equation of state
Read this section in the notes →What is the difference between extensive and intensive variables?
Extensive variables scale with the size of the system, such as volume, mass and internal energy; doubling the system doubles them. Intensive variables do not depend on size, such as pressure, temperature and density. Split a box of gas in equilibrium into two halves and each half keeps the same pressure and temperature, but has half the volume.
Quasi-static and isothermal processes
Read this section in the notes →What is a quasi-static process?
A quasi-static process is one carried out so slowly that the system stays practically in equilibrium at every step. Then pressure and temperature are well defined throughout, and the process can be drawn as a curve on a P-V diagram. Real processes are only approximately quasi-static, but the idea makes calculations possible.
Is there heat flow in an isothermal process?
Yes. Temperature is constant, so for an ideal gas ΔU = 0, and the first law then gives Q = W. When the gas expands it does work, so it must absorb an equal amount of heat from its surroundings; when compressed, it gives out heat. Constant temperature does not mean no heat exchange.
How do you find the work done in an isothermal expansion?
Use W = μRT ln(V₂/V₁), because pressure changes as the volume changes, so you cannot use PΔV. The formula comes from integrating P dV with P = μRT/V. For an expansion V₂ is larger than V₁, so the work done by the gas is positive.
Adiabatic process
Read this section in the notes →What is the difference between an isothermal and an adiabatic process?
In an isothermal process temperature stays constant and heat flows in or out freely. In an adiabatic process no heat is exchanged, so the temperature changes as the gas does work: it cools on expansion and warms on compression. Isothermal follows PV = constant; adiabatic follows PV^γ = constant, which is a steeper curve on a P-V diagram.
Why does a gas cool when it expands adiabatically?
With no heat entering, the work done by the expanding gas must come from its own internal energy, since ΔU = −ΔW. Less internal energy means a lower temperature. This is why air rushing out of a tyre valve feels cool, and why a sudden compression, such as in a bicycle pump, warms the gas.
Isochoric, isobaric and cyclic processes
Read this section in the notes →How is work calculated in an isobaric process?
At constant pressure, the work done by the gas is W = P(V₂ − V₁), which for an ideal gas equals μR(T₂ − T₁). This is the only process where the simple PΔV form is exact. In an isochoric process no work is done at all, since the volume does not change, so all heat goes into internal energy.
What is the change in internal energy in a cyclic process?
It is zero, because the system returns to its starting state and internal energy depends only on the state. The first law then gives Q_net = W_net: the net heat absorbed in one cycle equals the net work done. On a P-V diagram this work equals the area enclosed by the cycle.
Second law of thermodynamics
Read this section in the notes →Why can't any engine be 100% efficient?
By the second law, no process can convert heat entirely into work with no other effect. Every heat engine must reject some heat to a colder reservoir, so the work output is always less than the heat taken in. A refrigerator is limited in the same way: heat cannot flow from cold to hot without work being done.
Reversible and irreversible processes
Read this section in the notes →What makes a process irreversible?
A process is irreversible if it cannot be retraced so that both the system and its surroundings return exactly to their original states. Friction, viscosity, heat flow across a finite temperature difference, and sudden free expansion all make processes irreversible. Every real process is irreversible to some degree; reversible ones are useful idealisations.
Carnot engine
Read this section in the notes →Why is the Carnot engine the most efficient engine?
Because it runs on a fully reversible cycle of two isothermal and two adiabatic processes, with no losses to friction or heat flow across a finite temperature difference. Carnot's theorem states that no engine working between the same two temperatures can exceed its efficiency, η = 1 − T₂/T₁. It sets an upper limit that real engines cannot reach.
Does the efficiency of a Carnot engine depend on the working substance?
No. A Carnot engine's efficiency depends only on the temperatures of the hot and cold reservoirs, η = 1 − T₂/T₁, with both in kelvin. Whether the working substance is air, steam or any other material makes no difference. Celsius temperatures must never be used here, as they give the wrong ratio.
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